Adiabatic channel general potentials

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

In principle, the most general representation of the matrix elements of equation (68) includes a many-body expansion with one-, two-, and three-body terms. However, only two conditions [(a) and (b) in equations (66), (67)] may be used in the determination of the one- and two-body energy terms. If more conditions were to exist, the dimension of the matrix necessary to represent the adiabatic potential would be larger.16 In what follows we shall argue that the definition of V12 must depend on the type of conical intersection, namely on whether its locus is finite or infinite in extent (Section II.C). For the cases of HzO and 03 [equations (66), (67)] the conical intersection occurs along the C projection line, but only for finite values of the molecular perimeter (for H20, there is also a simple intersection at the O + H2 asymptotic channel, which is avoided for finite values of the OH distances117). For example, one gets for the linear dissociation of 03... 

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